Since T is an economy award ticket, the answer is no. They will tell you "if you wanted business, then you should have made a business award ticket."
Not quite sure I understand what you're saying. By that logic they would say the same on a revenue ticket and there would be no point to the upgrade certificate.
I don't see where it says that award tickets are excluded, and T is not in their list of exclusions. Nor is U for upgrade to F.